To find the solution set of the equation 2x² + 15 = 0, we start by isolating x². First, we subtract 15 from both sides:
2x² = -15
Next, we divide both sides by 2:
x² = -7.5
At this point, we can see that x² is equal to a negative number. Since the square of any real number is non-negative, there are no real solutions to the equation. However, we can find complex solutions by taking the square root of -7.5.
Using the imaginary unit ‘i’ (where i = √-1), we can express the solutions as follows:
x = ±√-7.5 = ±√(7.5)i = ±√(15/2)i = ±(√15/√2)i = ±(√30/2)i
Thus, the solution set in terms of complex numbers is:
x = ±(√30/2)i
In conclusion, the solution set of 2x² + 15 = 0 is a pair of complex numbers, and there are no real solutions.